A parameterized algorithm for the Maximum Agreement Forest problem on multiple rooted multifurcating trees

Shi, Feng; Chen, Jianer; Qi, Feng; Wang, Jianxin

doi:10.1016/j.jcss.2018.03.002

Cited by 13 publications

(9 citation statements)

References 41 publications

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“…The analysis in [1] made heavy use of a powerful abstraction known as an agreement forest, which in a nutshell partitions the two trees into smaller, non-overlapping fragments which do have the same topology in both trees (see e.g. [14,16] for overviews of algorithmic results and [2] for extremal results). Via a different technique, based on bounded search trees, running times of O(4 k • poly(|X|)) [16] and then O (3 k • poly(|X|)) were later obtained [5].…”

Section: Introductionmentioning

confidence: 99%

New Reduction Rules for the Tree Bisection and Reconnection Distance

Kelk

Linz

2020

Ann. Comb.

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Recently it was shown that, if the subtree and chain reduction rules have been applied exhaustively to two unrooted phylogenetic trees, the reduced trees will have at most $$15k-9$$ 15 k - 9 taxa where k is the TBR (Tree Bisection and Reconnection) distance between the two trees, and that this bound is tight. Here, we propose five new reduction rules and show that these further reduce the bound to $$11k-9$$ 11 k - 9 . The new rules combine the “unrooted generator” approach introduced in Kelk and Linz (SIAM J Discrete Math 33(3):1556–1574, 2019) with a careful analysis of agreement forests to identify (i) situations when chains of length 3 can be further shortened without reducing the TBR distance, and (ii) situations when small subtrees can be identified whose deletion is guaranteed to reduce the TBR distance by 1. To the best of our knowledge these are the first reduction rules that strictly enhance the reductive power of the subtree and chain reduction rules.

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Section: Introductionmentioning

confidence: 99%

New Reduction Rules for the Tree Bisection and Reconnection Distance

Kelk

Linz

2020

Ann. Comb.

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“…Because of its applications to the design of communication networks and water supply systems [2], MIST has been explored in the fields of parameterized computation and approximation algorithms. Parameterized computation, a clever method of dealing with NP-hard problems [3][4][5] has been extensively researched and applied in multiple fields [6][7][8][9][10][11]. The parameterized version of MIST is the k-internal spanning tree (k-IST) problem.…”

Section: Introductionmentioning

confidence: 99%

Incremental algorithms for the maximum internal spanning tree problem

Zhu

Yang

et al. 2021

Sci. China Inf. Sci.

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The maximum internal spanning tree (MIST) problem is utilized to determine a spanning tree in a graph G, with the maximum number of possible internal vertices. The incremental maximum internal spanning tree (IMIST) problem is the incremental version of MIST whose feasible solutions are edge-sequences e 1 , e 2 , . . . , e n−1 such that the first k edges form trees for all k ∈|In(T k )| with lower being better. Here, opt(G, k) denotes the number of internal vertices in a tree with k edges in G, which has the largest possible number of internal vertices, and |In(T k )| is the number of internal vertices in the tree comprising the solution's first k edges. We first obtained an IMIST algorithm with a competitive ratio of 2, followed by a 12/7-competitive algorithm based on an approximation algorithm for MIST.

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“…We will aggregate these factors and construct a general prediction model to the resolve reserve prediction problem for bank outlets. We also will consider how to use new techniques to improve the predicting performances, such as parameterized algorithm [16,17] and matrix completion [18,19] .…”

Section: Discussionmentioning

confidence: 99%

LSTM based reserve prediction for bank outlets

Liu

Dong

et al. 2019

Tinshhua Sci. Technol.

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Reserve allocation is a significant problem faced by commercial banking businesses every day. To satisfy the cash requirement of customers and abate the vault cash pressure, commercial banks need to appropriately allocate reserves for each bank outlet. Excessive reserve would impact the revenue of bank outlets. Low reserves cannot guarantee the successful operation of bank outlets. Considering the reserve requirement is effected by the past cash balance, we deal the reserve allocation problem as a time series prediction problem, and the Long Short Time Memory (LSTM) network is adapted to solve it. In addition, the proposed LSTM prediction model regards date property, which can affect the cash balance, as a primary factor. The experiment results show that our method outperforms some existing traditional methods.

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A parameterized algorithm for the Maximum Agreement Forest problem on multiple rooted multifurcating trees

Cited by 13 publications

References 41 publications

New Reduction Rules for the Tree Bisection and Reconnection Distance

New Reduction Rules for the Tree Bisection and Reconnection Distance

Incremental algorithms for the maximum internal spanning tree problem

LSTM based reserve prediction for bank outlets

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